Singles

Hidden Single

A Hidden Single is a digit that has only one possible cell left in a row, column or box, so it must go there — even if that cell still lists other candidates. To find one, pick a unit and a digit it is missing, strike every cell of the unit that already sees that digit in its row, column or box, and place the digit if exactly one cell survives. It is the digit's-eye twin of Naked Single, which asks instead what one cell can still hold.

What you need to see on the grid

Look for Hidden Singles from the first move to the last: right after every placement, around the digit you just wrote, and whenever no cell is down to one candidate. Four terms carry the method:

Unit: A row, a column or a box — 27 in all. A Hidden Single is always a statement about one unit: the same digit can have one place in a box and three in the row that crosses it, as in step 3 below.
Places of a digit: The empty cells of the unit where the digit can still go. You count cells, not candidates: one place means place the digit; two or more means try another digit or another unit, and come back later.
Blocked cell: An empty cell whose row, column or box already holds the digit. In a box the blockers come from the rows and columns crossing it; in a row, from the columns and boxes; in a column, from the rows and boxes. Striking blocked cells by eye is the cross-hatching of the Scanning lesson.
Hidden, not naked: A Naked Single is a cell with one candidate left: you find it by looking at a cell. A Hidden Single is a digit with one place left: you find it by looking at a digit inside a unit, and its cell may still list several candidates — they hide it. One cell can be both, but the two questions are different.

How to apply it, step by step

One position runs through all five steps — a box, then a row, then a column of the same puzzle. No cell in it is down to a single candidate, so a hunt for Naked Singles finds nothing here; every move below is a Hidden Single. Every diagram shows the whole grid. The cells a step needs are filled in; the others are left blank and hatched, so you know you can ignore them.

Step 1Pick a unit and a digit it is still missing

A Hidden Single is always found inside one unit — a row, a column or a box — so choose the unit first and stay in it. Box 8 is a good start: it already holds 3, 4, 5 and 8, so it is missing 1, 2, 6, 7 and 9, one digit for each of its five empty cells.

Then take one of the missing digits. The best bets are digits that already appear in the rows and columns crossing the unit, because every copy there rules out cells. Here that is 7, and the question is now precise: where in box 8 can 7 still go?

Only box 8 matters here: four digits placed, five cells empty. 7 is one of the five digits the box is still missing.
	C1	C2	C3	C4	C5	C6	C7	C8	C9
R1
R2
R3
R4
R5
R6
R7				3	8
R8						5
R9				4

Digit already on the grid
Box 8, the unit being checked
Candidate 7, the digit studied
Not needed for this step

Filled in: box 8. The other 72 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.

Step 2Strike every cell that already sees that digit

A cell of the unit is out if a 7 already sits in its row, its column or its box. Box 8 has no 7 of its own, so look along the rows and columns that cross it. Column 6 has a 7 at R5C6, so R7C6 and R9C6 are out. Row 8 has a 7 at R8C8, so R8C4 and R8C5 are out.

One cell survives: R9C5, whose row 9 and column 5 hold no 7 yet. With complete pencil marks you see the same thing directly — 7 is pencilled in R9C5 only. Striking cells by eye is how you find it without marks, and how you check marks you do not fully trust.

Box 8 and the two 7s that block it: R5C6 in column 6 and R8C8 in row 8. Four empty cells are struck; only R9C5 can still take 7.
	C1	C2	C3	C4	C5	C6	C7	C8	C9
R1
R2
R3
R4
R5						7
R6
R7				3	8
R8						5		7
R9				4

Digit already on the grid
Box 8, the unit being checked
Row or column holding a 7: its cells in box 8 are blocked
The one place left for 7
Candidate 7, the digit studied
Not needed for this step

Filled in: box 8; cells R5C6 and R8C8. The other 70 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.

Step 3One cell left: place the digit there

Box 8 must contain a 7 somewhere, and R9C5 is the only cell that can take it, so R9C5 = 7. That is the whole technique: one unit, one digit, one place left.

Now look back at R9C5 in step 2. It lists 1, 2, 6, 7 and 9, so nothing about the cell stands out — that is why this single is called hidden, and why a hunt for cells with one candidate (a Naked Single) walks straight past it. The other units do not show it either: in row 9, 7 still has three places (C1, C3, C5), and in column 5 three as well (R1, R3, R9). Only the box sees it. The cell's four other candidates do not matter: once the 7 has to go here, they are simply gone.

Technique: Hidden Single

Box 8, with row 9 and column 5 running through R9C5. In the box 7 has one place, so R9C5 = 7; in the row and in the column it still has three places each.
	C1	C2	C3	C4	C5	C6	C7	C8	C9
R1
R2					5
R3
R4
R5					4
R6
R7				3	8
R8						5
R9		5		4	7		3

Digit already on the grid
Box 8: one place left for 7
The cell that must be 7
Candidate 7, the digit studied
Digit placed
Not needed for this step

Filled in: row 9; column 5; box 8. The other 60 cells are left blank: they are not needed for this step. Placed: R9C5 = 7.

Step 4Do the same in a row or a column

Rows and columns work exactly the same way; only the blockers come from elsewhere. A cell of a row is struck by the digit in its column or in its box. Take row 5 and the digit 3, which the row is missing. R4C1 = 3 strikes R5C1, R5C2 and R5C3 at once, because they share box 4 with it. R7C4 = 3 strikes R5C4 through column 4, and R9C7 = 3 strikes R5C7 through column 7.

Only R5C9 is left, so R5C9 = 3 — a Hidden Single in a row. It was there from the start; box 8 came first only because boxes are the easiest units to scan. When the hint in the app looks for a Hidden Single, it checks in the same order: boxes, then rows, then columns.

Technique: Hidden Single

Row 5 and the three 3s that block it: R4C1 (box 4), R7C4 (column 4) and R9C7 (column 7). Five empty cells are struck; R5C9 is the only place left for 3.
	C1	C2	C3	C4	C5	C6	C7	C8	C9
R1
R2
R3
R4	3
R5					4	7		8	3
R6
R7				3
R8
R9							3

Digit already on the grid
Row 5, the unit being checked
Column or box holding a 3: its cells in row 5 are blocked
The cell that must be 3
Candidate 3, the digit studied
Digit placed
Not needed for this step

Filled in: row 5; cells R4C1, R7C4 and R9C7. The other 69 cells are left blank: they are not needed for this step. Placed: R5C9 = 3.

Step 5Collect what the placement unlocks

Every digit you place changes three units, so look around it before moving on. Writing 3 into R5C9 does two things: 3 leaves the pencil marks of every cell that sees R5C9, and R5C9 itself stops being a place for any other digit. The second effect is the one players forget.

Check column 9 for 5. R2C9 and R4C9 are struck by the 5s in their rows, R2C5 and R4C4; R7C9, R8C9 and R9C9 by the 5 at R7C7 in their box. Before step 4 that left 5 two places: R6C9, and R5C9, whose row, column and box 6 hold no 5. Now R5C9 is taken, so R6C9 = 5 — a Hidden Single in a column, unlocked by the one before it. Box 6 still has two places for 5, R6C8 and R6C9, so only the column shows it.

Technique: Hidden Single

Column 9 after R5C9 = 3, the three 5s that block it — R2C5 (row 2), R4C4 (row 4), R7C7 (box 9) — and box 6, which holds no 5. R6C9 is the only place left for 5 in the column.
	C1	C2	C3	C4	C5	C6	C7	C8	C9
R1									6
R2					5
R3									1
R4				5				4
R5								8	3
R6									5
R7							5
R8
R9

Digit already on the grid
Column 9, the unit being checked
Row or box holding a 5: its cells in column 9 are blocked
The cell that must be 5
Candidate 5, the digit studied
Digit placed
Not needed for this step

Filled in: column 9; box 6; cells R2C5, R4C4 and R7C7. The other 63 cells are left blank: they are not needed for this step. Placed: R6C9 = 5.

Common mistakes

Waiting for the cell to show one candidate

That is a Naked Single, a different move. A Hidden Single is placed while its cell still lists other digits — R9C5 above listed five — so if you only ever fill cells showing one pencil mark, you will stall on grids that still have easy moves left.

Counting from incomplete pencil marks

The count only means something over every empty cell of the unit. An empty cell you have not pencilled yet, or a mark you forgot to write, looks like "no 7 here" and turns two places into one — and the 7 you then write is a guess that can break the grid. If a unit's marks are not complete, strike its cells by eye as in step 2 instead.

Checking only the boxes

Boxes are the easiest units to scan, so many players check the nine boxes and declare the grid stuck. The singles of steps 4 and 5 are found in a row and a column, and neither is a Hidden Single in its box — step 5 shows box 6 still giving 5 two places. A grid has 27 units: give the rows and columns their pass before reaching for a harder technique.

Recent daily puzzles that needed this technique

Learn the move, not just the digit

In a real game, when the next move is a Hidden Single, the hint in the app names its row, column or box and goes through every other empty cell of it, saying what already blocks the digit there — the strike-out of step 2, done for you.

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